z^2=-2izbar

Solution for z^2=-2izbar equation:

Simplifying
z2 = -2izbar

Solving
z2 = -2abirz

Solving for variable 'z'.

Reorder the terms:
2abirz + z2 = -2abirz + 2abirz

Combine like terms: -2abirz + 2abirz = 0
2abirz + z2 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(2abir + z) = 0

Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

Move all terms containing z to the left, all other terms to the right.

Simplifying
z = 0
Subproblem 2
Set the factor '(2abir + z)' equal to zero and attempt to solve:

Simplifying
2abir + z = 0

Solving
2abir + z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-2abir' to each side of the equation.
2abir + -2abir + z = 0 + -2abir

Combine like terms: 2abir + -2abir = 0
0 + z = 0 + -2abir
z = 0 + -2abir
Remove the zero:
z = -2abir

Simplifying
z = -2abir
Solution
z = {0, -2abir}